Systems of Equations--Substitution

Front

What is a system of equations?

Back

A system of equations is a set of two or more equations with the same variables. The solution is the point(s) where the equations intersect.

Front

What is the substitution method in solving systems of equations?

Back

The substitution method involves solving one equation for one variable and then substituting that expression into the other equation.

Front

How do you isolate a variable in an equation?

Back

To isolate a variable, you perform inverse operations to get the variable on one side of the equation and all other terms on the opposite side.

Front

What does it mean to solve for y in the equation x + 3y = 9?

Back

To solve for y, rearrange the equation to express y in terms of x: y = (9 - x)/3.

Front

What is the first step in using the substitution method?

Back

The first step is to solve one of the equations for one variable in terms of the other variable.

Front

If x = 3y, what is y in terms of x?

Back

y = x/3.

Front

How do you check if a solution is correct for a system of equations?

Back

Substitute the solution back into both original equations to see if both equations are satisfied.

Front

What is the solution to the system of equations x + 3y = 9 and 2x + y = -2?

Back

The solution is (-3, 4).

Front

What is the solution to the system of equations 2y + x = -15 and x = 3y?

Back

The solution is (-9, -3).

Front

What is the solution to the system of equations y = 3x - 13 and 2x + 4y = 4?

Back

The solution is (4, -1).